Question

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Answer 1

`9^{-(1)/(2)}=(1)/(3)`

Given:

`9^{-(1)/(2)}`

To evaluate this, we must be familiar with two exponent rules.

The first one is, the negative exponent tells us that a number with a negative exponent should be put to the denominator or vice versa. Therefore, we can rewrite the given expression as:

`\frac{1}{9^{(1)/(2)}}`

Then, fractional exponents states that:

`a^{(m)/(n)}=\sqrt[n]{a^m}`

Since we have m = 1, and n = 2, we can rewrite the expression as:

`\frac{1}{\sqrt[2]{9^1}}=\frac{1}{\sqrt[]{9}}`

Next, we simplify this equation by getting the square root of 9, which is 3. Therefore, the final expression would be:

`(1)/(3)`